The broad objective of the proposed research is to develop the theory of the dynamics of real Mendelian populations. The importance of the mathematical and statistical behavior of genetic populations has been exemplified by the early early work of Wright, Fischer, and Haldane, and by much recent work by Kimura, Crow, Lewontin, Karlin, Ewens and others. The need for development of more realistic models is well known to biologists. Deficiencies of present knowledge revolve around the definition and use of concepts of fitness, the lack of a detailed model involving several components of fitness (fertility of mating, viability of young, etc.), the role of in-breeding and mating system, and the effect of overlapping of generations. The whole program of work involves a combination of mathematical probability, often at a deep level except for the very elementary models, mathematical theory of deterministic linear and non-linear systems, and techniques of statistical inference for data interpretation. The comprehensive progress report describes the attacks which have been made on problems. In essentially all the aspects investigated, the results that are reported are initial and preliminary. Essentially all the subtopics need additional extensive research.